In classification problems, the label space $\mathbf{Y}$ is finite. In binary classification problems, its size is 2; usually, $\mathbf{Y}=\{0,1\}$ or $\mathbf{Y}=\{-1,1\}$. Allowed forecasts in such problems are elements of $\mathbf{Y}$ (we will have a probabilistic classification problem if we allow probability measures on $\mathbf{Y}$ as forecasts).